A Domain of Spacetime Intervals in General Relativity |
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Authors: | Keye Martin Prakash Panangaden |
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Affiliation: | (1) Naval Research Laboratory, Center for High Assurance Computer Systems, Washington, DC 20375, USA;(2) School of Computer Science, McGill University, Montreal, Quebec, H3A 2A7, Canada |
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Abstract: | We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emerges from something discrete. |
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